Hill A
Proc R Soc Lond B Biol Sci. 1982 May 22;215(1199):155-74. doi: 10.1098/rspb.1982.0035.
A theory is advanced that volume transfer across a membrane pore during osmosis takes place in two modes: if solute is sterically excluded from the pore a pressure gradient is set up and viscous flow of solvent results; if solute can enter the pore then osmotic flow is a diffusive phenomenon, and there is no pressure gradient in any part of the pore to which solute has access, even at low concentration due to a repulsive wall field. As a consequence the reflexion coefficients sigma s and sigma f for osmosis and ultrafiltration are not equal, although equality is usually assumed to result from an underlying thermodynamic reciprocity; instead, the two coefficients represent essentially different processes. These results follow from three basic thermodynamic considerations which have usually been overlooked: (i) there is a qualitative difference between a permeable pore and an impermeable one, the latter having a discontinuity of solute activity at the mouth, which the former does not; (ii) the osmotic pressure within the pore is determined by the activity of solute not the concentration; (iii) the effective resistance to flow through a channel depends upon the nature of the régime, being different for diffusive and viscous flow. An expression for sigma s is derived and shown to be compatible with experimental data on polymer membranes and homoporous bilayers.
一种理论认为，在渗透过程中跨膜孔的体积传递以两种模式发生：如果溶质在空间上被排除在孔外，就会建立起压力梯度并导致溶剂的粘性流动；如果溶质能够进入孔中，那么渗透流就是一种扩散现象，并且在溶质能够进入的孔的任何部分都不存在压力梯度，即使在低浓度时由于排斥壁场也是如此。因此，渗透和超滤的反射系数σs和σf并不相等，尽管通常认为相等是由潜在的热力学互易性导致的；相反，这两个系数代表了本质上不同的过程。这些结果源于三个通常被忽视的基本热力学考虑因素：（i）可渗透孔和不可渗透孔之间存在质的差异，后者在孔口处溶质活性有间断，而前者没有；（ii）孔内的渗透压由溶质的活度而非浓度决定；（iii）通过通道的有效流动阻力取决于流态的性质，对于扩散流和粘性流是不同的。推导了σs的表达式，并表明它与聚合物膜和均孔双层膜的实验数据相符。
